diamond

hyppo.tools.diamond(n, p, noise=False, low=- 1, high=1)

Diamond simulation.

Diamond $(X, Y) \in \mathbb{R}^p \times \mathbb{R}^p$: $U \sim \mathcal{U}(-1, 1)$, $V \sim \mathcal{N}(0, 1)^p$, $\theta = -\frac{\pi}{4}$,

$$\begin{split}X_{|d|} &= U \cos(\theta) + V \sin(\theta) + 0.05 p \epsilon_{|d|}\ \mathrm{for}\ d = 1, ..., p \\ Y_{|d|} &= -U \sin(\theta) + V \cos(\theta)\end{split}$$

Parameters

• n (int) -- The number of samples desired by the simulation (>= 5).

• p (int) -- The number of dimensions desired by the simulation (>= 1).

• noise (bool, default: False) -- Whether or not to include noise in the simulation.

• low (float, default: -1) -- The lower limit of the uniform distribution simulated from.

• high (float, default: 1) -- The upper limit of the uniform distribution simulated from.

Returns

x,y (ndarray) -- Simulated data matrices. x` and ``y have shapes (n, p) and (n, p) where n is the number of samples and p is the number of dimensions.